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Proof step 81 from proof inv-link (previous step)

dirs0[ino1] = mkdir(m5, md2, # links(ino1, dirs0), m10, entries1), entries[str] = entries2[str], dirs0[ino0] = mkdir(m2, md1, # links(ino0, dirs0), m8, entries), entries0[str] = entries2[str], files0[entries2[str]] = mkfile(m0, md6, # links(entries2[str], dirs0), content0), dirs0[m] = mkdir(m1, md5, # links(m, dirs0), m9, entries3), dirs0[ino2] = mkdir(m4, md3, # links(ino2, dirs0), m6, entries0), entries1[str] = entries2[str], dirs0[ino3] = mkdir(m7, md4, # links(ino3, dirs0), m12, entries2), err = ESUCCESS, afs-cons(dirs0, files0), afs-cons (dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m3, md0, # links(entries2[str], dirs0) + 1, content0)]), dcache-cons(dcache, dirs0, files0), icache-cons(icache, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache, pcache), str ∈ entries1, ino1 ∈ dirs0, str ∈ entries, ino0 ∈ dirs0, ino2 ∈ dirs0, str ∈ entries0, ino3 ∈ dirs0, str ∈ entries2, m ∈ dirs0, entries2[str] ∈ files0, ¬ str0 ∈ entries3, asynced1 → synced(files0, icache, pcache), links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(ino3, dirs0) ≠ ∅ ∨ ino3 = ROOT_INO ⊦ ⟪icache_set# (mkinode (m, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].meta, true, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].nlink, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].nsubdirs, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].size), false ; err, icache); icache_set# (getinode (mkdentry(str, entries0[str]).ino, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)][entries1[str]] .size:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).size ] [entries1[str] ] .meta:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).meta ]), false ; err, icache); dcache_set# ((m ∈ dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])] ⊃ mkinode (m, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].meta, true, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].nlink, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].nsubdirs, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].size) ;mkinode (m, files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)][entries1[str]] .size:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).size ] [entries1[str] ] .meta:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).meta ] [m ] .meta, false, files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)][entries1[str]] .size:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).size ] [entries1[str] ] .meta:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).meta ] [m ] .nlink, 0, files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)][entries1[str]] .size:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).size ] [entries1[str] ] .meta:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).meta ] [m ] .size) ) .ino, mkdentry(str0, mkdentry(str, entries0[str]).ino).name, mkdentry(str0, mkdentry(str, entries0[str]).ino) ; err, dcache)⟫ ( icache-cons (icache, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], mkfile(m3, md0, # links(entries2[str], dirs0) + 1, content0) ]) ∧ dcache-cons (dcache, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], mkfile(m3, md0, # links(entries2[str], dirs0) + 1, content0) ]) ∧ pcache-cons (pcache, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], mkfile(m3, md0, # links(entries2[str], dirs0) + 1, content0) ]) ∧ synced(dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])], icache, pcache) ∧ ( asynced1 → synced (files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], mkfile(m3, md0, # links(entries2[str], dirs0) + 1, content0) ], icache, pcache)))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 82:
(m ∈ dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])] ⊃ mkinode (m, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].meta, true, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].nlink, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].nsubdirs, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].size) ;mkinode (m, files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)][entries1[str]] .size:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).size ] [entries1[str] ] .meta:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).meta ] [m ] .meta, false, files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)][entries1[str]] .size:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).size ] [entries1[str] ] .meta:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).meta ] [m ] .nlink, 0, files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)][entries1[str]] .size:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).size ] [entries1[str] ] .meta:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).meta ] [m ] .size) ) = mkinode(m11, md7, boolvar, m13, m14, m15), dirs0[ino3] = mkdir(m7, md4, # links(ino3, dirs0), m12, entries2), entries1[str] = entries2[str], dirs0[ino2] = mkdir(m4, md3, # links(ino2, dirs0), m6, entries0), dirs0[m] = mkdir(m1, md5, # links(m, dirs0), m9, entries3), files0[entries2[str]] = mkfile(m0, md6, # links(entries2[str], dirs0), content0), entries0[str] = entries2[str], dirs0[ino0] = mkdir(m2, md1, # links(ino0, dirs0), m8, entries), entries[str] = entries2[str], dirs0[ino1] = mkdir(m5, md2, # links(ino1, dirs0), m10, entries1), err = ESUCCESS, afs-cons (dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m3, md0, # links(entries2[str], dirs0) + 1, content0)]), afs-cons(dirs0, files0), dcache-cons(dcache, dirs0, files0), icache-cons(icache, dirs0, files0), pcache-cons(pcache, dirs0, files0), synced(dirs0, icache, pcache), entries2[str] ∈ files0, m ∈ dirs0, str ∈ entries2, ino3 ∈ dirs0, str ∈ entries0, ino2 ∈ dirs0, ino0 ∈ dirs0, str ∈ entries, ino1 ∈ dirs0, str ∈ entries1, asynced1 → synced(files0, icache, pcache), links(ino3, dirs0) ≠ ∅ ∨ ino3 = ROOT_INO, links(m, dirs0) ≠ ∅ ∨ m = ROOT_INO, links(ino2, dirs0) ≠ ∅ ∨ ino2 = ROOT_INO, links(ino0, dirs0) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino1, dirs0) ≠ ∅ ∨ ino1 = ROOT_INO ⊦ ⟪icache_set# (mkinode (m, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].meta, true, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].nlink, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].nsubdirs, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])][m].size), false ; err, icache); icache_set# (getinode (mkdentry(str, entries0[str]).ino, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)][entries1[str]] .size:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).size ] [entries1[str] ] .meta:= mkinode(entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3).meta ]), false ; err, icache); dcache_set#(m11, mkdentry(str0, mkdentry(str, entries0[str]).ino).name, mkdentry(str0, mkdentry(str, entries0[str]).ino); err, dcache)⟫ ( icache-cons (icache, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], mkfile(m3, md0, # links(entries2[str], dirs0) + 1, content0) ]) ∧ dcache-cons (dcache, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], mkfile(m3, md0, # links(entries2[str], dirs0) + 1, content0) ]) ∧ pcache-cons (pcache, dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])], files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], mkfile(m3, md0, # links(entries2[str], dirs0) + 1, content0) ]) ∧ synced(dirs0[m, mkdir(m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]])], icache, pcache) ∧ ( asynced1 → synced (files0[entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0)] [entries1[str], mkfile(m3, md0, # links(entries2[str], dirs0) + 1, content0) ], icache, pcache))), str0 ∈ entries3

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [( m ∈ dirs0 [m, mkdir (m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]]) ] ⊃ mkinode (m, dirs0 [m, mkdir (m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]]) ] [m ] .meta, true, dirs0 [m, mkdir (m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]]) ] [m ] .nlink, dirs0 [m, mkdir (m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]]) ] [m ] .nsubdirs, dirs0 [m, mkdir (m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]]) ] [m ] .size) ;mkinode (m, files0 [entries2[str], mkfile (m0, md6, # links(entries2[str], dirs0) + 1, content0) ] [entries1[str], files0 [entries2[str], mkfile (m0, md6, # links(entries2[str], dirs0) + 1, content0) ] [entries1[str], files0 [entries2[str], mkfile (m0, md6, # links(entries2[str], dirs0) + 1, content0) ] [entries1[str] ] .size:= mkinode (entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3) .size ] [entries1[str] ] .meta:= mkinode (entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3) .meta ] [m ] .meta, false, files0 [entries2[str], mkfile (m0, md6, # links(entries2[str], dirs0) + 1, content0) ] [entries1[str], files0 [entries2[str], mkfile (m0, md6, # links(entries2[str], dirs0) + 1, content0) ] [entries1[str], files0 [entries2[str], mkfile (m0, md6, # links(entries2[str], dirs0) + 1, content0) ] [entries1[str] ] .size:= mkinode (entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3) .size ] [entries1[str] ] .meta:= mkinode (entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3) .meta ] [m ] .nlink, 0, files0 [entries2[str], mkfile (m0, md6, # links(entries2[str], dirs0) + 1, content0) ] [entries1[str], files0 [entries2[str], mkfile (m0, md6, # links(entries2[str], dirs0) + 1, content0) ] [entries1[str], files0 [entries2[str], mkfile (m0, md6, # links(entries2[str], dirs0) + 1, content0) ] [entries1[str] ] .size:= mkinode (entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3) .size ] [entries1[str] ] .meta:= mkinode (entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3) .meta ] [m ] .size) ), m11, md7, boolvar, m13, m14, m15]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: ( m ∈ dirs0 [m, mkdir (m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]]) ] ⊃ mkinode (m, dirs0 [m, mkdir (m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]]) ] [m ] .meta, true, dirs0 [m, mkdir (m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]]) ] [m ] .nlink, dirs0 [m, mkdir (m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]]) ] [m ] .nsubdirs, dirs0 [m, mkdir (m1 + 1, md, # links(m, dirs0), m9, entries3[str0, entries2[str]]) ] [m ] .size) ;mkinode (m, files0 [entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0) ] [entries1[str], files0 [entries2[str], mkfile (m0, md6, # links(entries2[str], dirs0) + 1, content0) ] [entries1[str], files0 [entries2[str], mkfile (m0, md6, # links(entries2[str], dirs0) + 1, content0) ] [entries1[str] ] .size:= mkinode (entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3) .size ] [entries1[str] ] .meta:= mkinode (entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3) .meta ] [m ] .meta, false, files0 [entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0) ] [entries1[str], files0 [entries2[str], mkfile (m0, md6, # links(entries2[str], dirs0) + 1, content0) ] [entries1[str], files0 [entries2[str], mkfile (m0, md6, # links(entries2[str], dirs0) + 1, content0) ] [entries1[str] ] .size:= mkinode (entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3) .size ] [entries1[str] ] .meta:= mkinode (entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3) .meta ] [m ] .nlink, 0, files0 [entries2[str], mkfile(m0, md6, # links(entries2[str], dirs0) + 1, content0) ] [entries1[str], files0 [entries2[str], mkfile (m0, md6, # links(entries2[str], dirs0) + 1, content0) ] [entries1[str], files0 [entries2[str], mkfile (m0, md6, # links(entries2[str], dirs0) + 1, content0) ] [entries1[str] ] .size:= mkinode (entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3) .size ] [entries1[str] ] .meta:= mkinode (entries1[str], md0, false, # links(entries1[str], dirs0), 0, m3) .meta ] [m ] .size) ), m11, md7, boolvar, m13, m14, m15